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G-2D-1-2

Page history last edited by Brenda Butz 6 years, 3 months ago

G.2D.1.2 Apply the properties of angles, including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve real-world and mathematical problems using algebraic reasoning and proofs.

In a Nutshell

In this standard students will be able to define, draw and apply to given situations the angle pair relationships that are used most often in geometry. Being able to recognize these basic relationships within a more complex situation or diagram will assist students in breaking down a problem into more readily solvable pieces.

Student Actions	Teacher Actions
Develop a Deep and Flexible Understanding: Students will correctly identify angle pairs and use the relationships in a variety of diagrams and tasks. Develop Strategies for Problem Solving: Students will analyze diagrams and verbal descriptions to apply angle relationships in a variety of tasks. Develop Mathematical Reasoning: Students will use mathematically correct methods when applying previously learned algebraic concepts to a geometric relationship and/or a real world situation. Develop the Ability to Make Conjectures, Model, and Generalize: Students will make conjectures, model tasks, and generalize problems in order to prove a variety of angle relationships.	Teachers will implement tasks that will promote productive struggle and give the students the chance to practice problems relating to geometric relationships from basic to more complex angle relationships. Teachers will use multiple representations to connect geometric diagrams to algebraic methods. Teachers will build procedural fluency from conceptual understanding by applying algebra concepts to angle pair relationships.
Key Understandings	Misconceptions
Students understand the properties of parallel lines and the angle pair relationships that are formed by a transversal. Students understand how to determine if two lines are parallel. Students understand the properties of perpendicular lines and how to apply them to real world situations.	Students think that all angle pairs are congruent i.e. same side interior angles. Students assume angle pairs are congruent or supplementary before knowing lines are parallel. Students believe vertical angles and linear pairs prove parallel lines.